N=4 Gauged Supergravity from Duality-Twist Compactifications of String Theory

TL;DR

This paper explores how certain four-dimensional gauged supergravities can be derived from string theory compactifications on SU(2)-structure manifolds, including geometric, flux, and non-geometric backgrounds, and establishes dualities with heterotic string theory.

Contribution

It demonstrates the realization of specific gauged supergravities from IIA string theory on SU(2)-structure manifolds and introduces new heterotic T-fold backgrounds with a generalized sigma model formalism.

Findings

Identification of SU(2)-structure compactifications as K3 fibrations over T^2.

Construction of non-geometric Mirror-fold backgrounds.

Introduction of new heterotic T-fold backgrounds with a generalized formalism.

Abstract

We investigate the lifting of half-maximal four-dimensional gauged supergravities to compactifications of string theory. It is shown that a class of such supergravities can arise from compactifications of IIA string theory on manifolds of SU(2)-structure which may be thought of as K3 fibrations over T^2. Examples of these SU(2)-structure backgrounds, as smooth K3 bundles and as compactifications with H-flux, are given and we also find evidence for a class of non-geometric, Mirror-fold backgrounds. By applying the duality between IIA string theory on K3 and Heterotic string theory on T^4 fibrewise, we argue that these SU(2)-structure backgrounds are dual to Heterotic compactifications on a class T^4 fibrations over T^2. Examples of these fibrations as twisted tori, H-flux and T-fold compactifications are given. We also construct a new set of backgrounds, particular to Heterotic string theory, which includes a previously unknown class of Heterotic T-folds. A sigma model description of these backgrounds, from the Heterotic perspective, is presented in which we generalize the Bosonic doubled formalism to Heterotic string theory.